Method and device for completing social network using artificial neural network

ABSTRACT

A device for completing a social network using an artificial neural network includes: a neural network unit configured to receive a target network having unrevealed missing nodes as input, infer the connections of the missing nodes with a neural network, and output multiple candidate complete networks according to various node sequences; and a selection unit configured to select one of the candidate complete networks outputted by the neural network unit, where the neural network unit outputs the candidate complete networks by using weights of a graph-generating neural network that has learned graph structures of reference networks having attributes similar to those of the target network, and the selection unit uses connection probability vectors obtained from the learned graph-generating neural network to select the candidate complete network probabilistically having a structure closest to that of the target network based on the connection probability vectors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. 119(a) to Korean PatentApplication No. 10-2019-0126749, filed with the Korean IntellectualProperty Office on Oct. 14, 2019, the disclosure of which isincorporated herein by reference in its entirety.

BACKGROUND 1. Technical Field

The present disclosure relates to completing a social network, moreparticularly to a method and device for completing a social networkusing an artificial neural network.

2. Description of the Related Art

With various types of social networking services provided in recenttimes, users can maintain various friend relationships over socialnetworking services. In a social network, the connections between usersmay be utilized for various purposes.

For example, the friend relationships between users can be used toidentify a user community, and such a community can be utilized for thepurpose of marketing targeted at certain users, analysis of userpreferences, downstream mining, and the like.

However, certain users may not reveal their friend relationships, andsuch unrevealed friend relationships make it difficult to identify thecomplete structure of a social network. Unrevealed friend relationshipsacts as obstacles to clearly identifying the structural characteristicsof a particular social network, and various attempts have been made toinfer unrevealed friend relationships.

Predicting the true network by inferring the unrevealed friendrelationships in a social network in this manner is referred to asnetwork completion. Since unrevealed friend relationships areinformation of which the true values cannot be known, there is aninherent limit to how accurately a network can be completed.

Various algorithms for network completion have been presented, of whicha representative method is the Kronecker based network completionmethod. However, the Kronecker based network completion method is usedunder the assumption that the network follows a pure power law, there isthe problem that the network completion may become very inaccurate ifthe network does not follow such a power law structure.

SUMMARY

An aspect of the disclosure proposes a method and device for networkcompletion using an artificial neural network that can overcome thelimit of social networks of being unable to obtain true data and caninfer missing nodes with comparatively high accuracy.

To achieve the objective above, an aspect of the disclosure provides anetwork completion device that includes: a neural network unitconfigured to receive a target network having unrevealed missing nodesas input, infer the connections of the missing nodes by way of a neuralnetwork, and output a multiple number of candidate complete networksaccording to various node sequences; and a selection unit configured toselect one of the multiple candidate complete networks outputted by theneural network unit, where the neural network unit outputs the multiplecandidate complete networks by using weights of a graph-generatingneural network that has learned graph structures of reference networkshaving attributes similar to those of the target network, and theselection unit uses connection probability vectors obtained from thelearned graph-generating neural network to select the candidate completenetwork probabilistically having a structure closest to that of thetarget network based on the connection probability vectors.

Sequence information that configures an arbitrary sequence for theobservable nodes and the missing nodes requiring inferring in the targetnetwork may be inputted to the neural network unit, and the neuralnetwork unit may output the candidate complete networks according to thesequence information.

The learned graph-generating neural network may configure the weights bylearning a function (f_(trans)) related to the topologies of thereference networks and a function (f_(out)) related to connectionprobability.

The learned graph-generating neural network may generate a graph byusing the function related to the topologies of the reference networksand the function related to the connection probability to sequentiallypaint nodes.

A connection probability vector may include probability informationrelated to connections of a graph topology generated by way of thegraph-generating neural network.

The selection unit may select one of the candidate complete networksbased on the equation shown below:

${\hat{G} = {\underset{G}{argmax}\mspace{14mu}{P\left( {{G❘G_{O}},\theta} \right)}}},$

where G represents the candidate complete networks, G_(O) represents theinputted target network, θ represents a connection probability vector,and Ĝ represents the selected candidate complete network.

Another aspect of the disclosure provides a network completion methodthat includes: (a) receiving a target network having unrevealed missingnodes as input, inferring connections of the missing nodes by way of aneural network, and outputting a multiple number of candidate completenetworks according to various node sequences; and (b) selecting one ofthe plurality of candidate complete networks outputted in step (a),where step (a) outputs the multiple candidate complete networks by usingweights of a graph-generating neural network that has learned a graphstructure of reference networks having attributes similar to those ofthe target network, and step (b) uses a connection probability vectorobtained from the learned graph-generating neural network to select acandidate complete network probabilistically having the structureclosest to that of the target network based on the connectionprobability vector.

An embodiment of the disclosure makes it possible to overcome the limitof social networks of being unable to obtain true data and makes itpossible to infer missing nodes with comparatively high accuracy.

Additional aspects and advantages of the present disclosure will be setforth in part in the description which follows, and in part will beobvious from the description, or may be learned by practice of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the structure of a typical social network.

FIG. 2 shows a matrix representing connections between the nodes formingthe social network illustrated in FIG. 1 .

FIG. 3 shows an example of a social network that includes unrevealedfriend relationships.

FIG. 4 illustrates a method of completing a network according to anembodiment of the disclosure.

FIG. 5 illustrates a structure for learning a network completion deviceaccording to an embodiment of the disclosure.

FIG. 6 is a diagram conceptually illustrating the inference process of agraph-generating neural network 500 according to an embodiment of thedisclosure.

FIG. 7 is a diagram conceptually illustrating structure of a networkcompletion neural network module 510 according to an embodiment of thedisclosure.

FIG. 8 shows an example of a graph completion process at a neuralnetwork unit 700 according to an embodiment of the disclosure.

DETAILED DESCRIPTION

A description of the present invention is provided below with referenceto the accompanying drawings. However, the invention can be implementedin many different forms and thus is not limited to the embodimentsdescribed herein.

For a clear description of the invention, parts of little relevance tothe descriptions have been omitted in the drawings, and throughout thespecification, like reference numerals have been designated to likeparts.

Throughout the specification, mention of a certain part being“connected” to another part includes not only cases of being “directlyconnected” but also cases of being “indirectly connected” by way ofanother member positioned in-between.

Also, mention of a certain part “including” a certain element does notpreclude the inclusion of other elements and can mean another elementcan be included additionally unless there is an explicit statement tothe contrary.

Certain embodiments of the disclosure are described below in greaterdetail with reference to the accompanying drawings.

FIG. 1 illustrates the structure of a typical social network, and FIG. 2shows a matrix representing connections between the nodes forming thesocial network illustrated in FIG. 1 .

Referring to FIG. 1 , each of the nodes shown in FIG. 1 is a userforming the social network. In FIG. 1 , a particular node is connectedwith other nodes. For example, node #1 is connected with node #2, node#3, and node #4, and the connections of the node mean that the user ofnode #1 has a friend relationship with the user of node #2, the user ofnode #3, and the user of node #4.

In a social network such as Facebook or Instagram, users are connectedin various relationships, and such connections between users offerinformation useful for discovering the user community. A communitydiscovered through the connections between users can be used for variousmarketing and information provision strategies.

In the matrix illustrated in FIG. 2 that represents the connectionsbetween network users, each column and each row represent a node number,where a mark of 1 means that there is a friend relationship between theusers corresponding to the column and row, while a mark of 0 means thatthere is no friend relationship between the users corresponding to thecolumn and row.

A network connection topology such as that illustrated in FIG. 1 can beexpressed in the form of vectors by way of a connection matrix such asthat shown in FIG. 2 .

However, quite a few social network users may refrain from revealingfriend relationships with other users. Thus, it may be difficult toaccurately identify a social network due to users who do not revealfriend relationships, and this may be a major cause of inaccuracy indiscovering a community. Inaccuracy in the discovery of a community canlead to inadequate marketing and information provision, and identifyingunrevealed friend relationships can be necessary for various reasons.

FIG. 3 shows an example of a social network that includes unrevealedfriend relationships.

In FIG. 3 , nodes expressed by solid lines are observable nodes (users),and nodes expressed by dotted lines are nodes that are hidden due tounrevealed friend relationships. In the present specification, anobservable node is defined a ‘visible node’, and a hidden node isdefined a ‘missing node’.

Typically when observing a network, only the visible nodes and therelationships between visible nodes are observed, and the presence ofmissing nodes and the connections of the missing nodes are not observed.

Recovering the unobserved missing nodes and the connections between themissing nodes is referred to as completing a network, and the presentdisclosure relates to such network completion. Ultimately, the presentdisclosure aims to recover the missing nodes and the connections betweenmissing nodes that are hidden in a particular social network in whichonly visible nodes are observed.

FIG. 4 illustrates a method of completing a network according to anembodiment of the disclosure.

The network shown on the left in FIG. 4 is the true network G_(T) and isa network in which the visible nodes and missing nodes as well as theconnections between all of the nodes are shown. The network G_(O) shownin the middle is the network that is actually observed. The missingnodes, marked with question marks, cannot actually be observed. FIG. 4illustrates an example in which two nodes are missing nodes.

The network completion intended by the present disclosure is to inferthe missing nodes and the connections of the missing nodes from thenetwork G_(O) in which the missing nodes are not observed, and thecompleted network is illustrated on the right in FIG. 4 .

The present disclosure recovers the missing nodes and the connections ofmissing nodes of a particular social network through an artificialneural network. The learning of a typical artificial neural network isperformed using label information named ‘ground truth’. However,obtaining label information for missing nodes and connections of themissing node may realistically be quite difficult. Therefore, thedisclosure proposes a method for completing a network that can recoverthe hidden missing nodes and the connections of the missing nodeswithout using ground truths.

FIG. 5 illustrates a structure for learning a network completion deviceaccording to an embodiment of the disclosure.

Referring to FIG. 5 , a network completion device according to anembodiment of the disclosure may perform learning by using agraph-generating neural network 500. The graph-generating neural network500 may be a neural network used conventionally for generating variousforms of graphs. An embodiment of the disclosure may regard a socialnetwork as a kind of graph and may learn the graph-generating neuralnetwork 500 to complete the network.

As the learning material for the learning of the graph-generating neuralnetwork 500, a reference social network may be utilized that hasattributes similar to those of the social network subject to networkrecovery. For example, if the social network subject to network recoveryis a social network of male students in a first university situated inSinchon, then another social network having similar attributes may beutilized as learning material. For example, a social network of malestudents in a second university situated in Sinchon may be utilized as areference network and utilized as the learning material for thegraph-generating neural network 500.

The graph-generating neural network 500 may use various reference socialnetworks inputted as learning material to learn the structure of socialnetworks having similar attributes. More specifically, thegraph-generating neural network 500 may output connection probabilityvectors θ through the learning. A connection probability vector may be avector that represents probability information of the connections ofnodes forming the network.

The specific structures of the connection probability vectors outputtedthrough the learning of the graph-generating neural network 500 and thedetailed learning method will be described with reference to separatedrawings.

After the learning at the graph-generating neural network 500 isfinished, the completion of the social network including missing nodesmay be performed at the network completion neural network module 510.The social network G_(O) that is the object of the completion may beinputted to the network completion neural network module 510. Theinputted social network may include only visible nodes and connectionsbetween the visible nodes, and the network completion neural networkmodule 510 may infer the missing nodes and the connections of themissing nodes from the inputted social network to perform networkcompletion.

The connection probability vectors obtained through the learning at thegraph-generating neural network 500 may be inputted to the networkcompletion neural network module 510, and the network completion neuralnetwork module 510 may infer the missing nodes and the connections ofthe missing nodes based on the connection probability vectors.

As described above, it may be difficult to acquire true data regardingunrevealed friend relationships, and the present disclosure may use thegraph-generating neural network 500 to perform network completion for asocial network having such properties. To this end, a social network maybe converted into vector information for graph generation, after whichlearning may be performed at the graph-generating neural network 500.Also, since there is no true data acquired, a social network for areference group having similar attributes may be learned in the form ofa graph at the graph-generating neural network 500.

The above provides an overview of the disclosure, described withreference to FIG. 5 , and the following provides a description on thespecific structures and operations of the graph-generating neuralnetwork 500 and the network completion neural network module 510.

FIG. 6 is a diagram conceptually illustrating the inference process of agraph-generating neural network 500 according to an embodiment of thedisclosure.

The graph-generating neural network 500 is not a neural network forlearning a network structure but rather a neural network for painting agraph. The graph-generating neural network 500 may be a neural networkthat infers the feature information of the learned graphs and learnsgraph painting based on the inferred feature information. An embodimentof the disclosure takes advantage of the fact that a network structureis similar to a graph structure and thus may use a graph-generatingneural network 500. Such use of the graph-generating neural network 500is an important feature of the disclosure.

The graph-generating neural network 500 may infer two types ofinformation based on the inputted network structure, where the two typesof information inferred include graph topology vectors and connectionprobability vectors.

A graph topology vector is a vector that represents the topologystructure of a graph. For example, in FIG. 6 , the final generated graphis a graph in which 1-2-4-3-1 are connected, and such a graph structurerepresented in vector form is a graph topology vector.

A connection probability vector is a vector related to probabilityinformation for connections of the nodes forming the graph. For example,in FIG. 6 , node #1 and node #2 are connected, and information on theprobability of node #1 and node #2 being connected may be included inthe connection probability vector, and the connection probabilityvectors may include probability information for all connections of thegraph.

The graph-generating neural network 500 may learn graph generation inthe manner of sequentially painting the nodes forming the graph, wherethe sequence of the painted nodes may be provided beforehand.

From the perspective of network completion, the total number of nodes ofthe graph that must be generated is the sum value of the number ofvisible nodes |V_(O)| and the number of missing nodes |V_(M)|. Here, thenumber of permutations for possible sequences of the nodes is(|V_(O)|+|V_(M)|)!.

The graph topology vector for a given node sequence may be expressed asEquation 1 shown below.S ^(π)

(S ₁ ^(π) , . . . ,S _(|V) _(O) _(|+|V) _(M) _(|) ^(π))  [Equation 1]

In Equation 1 above, the i of S_(i) ^(π) represents the indexes of thesequentially painted (generated) nodes, and S_(i) ^(π) is a vectorrepresenting the connections of nodes at the i-th sequence.

Referring to FIG. 6 , S₁ ^(π) begins at an empty set. The first node,node #1, may be generated at h1, and the connection of the subsequentlygenerated node may be recorded in S₂ ^(π). In FIG. 6 , S₂ ^(π) isdefined as {1}, and this means that the subsequently generated node willbe connected with node #1. Also, the probability information for theconnection of S₂ ^(π) may be recorded in θ₂. FIG. 6 illustrates anexample in which θ₂ is 0.9, which means that the probability of node #1and the subsequently generated node being connected is 0.9.

At h2, the next node, node #2, may be generated based on S₂ ^(π). SinceS₂ ^(π) is {1}, it can be seen from h2 that the subsequently generatednode #2 will be generated to be connected with node #1.

S₃ ^(π) is defined as {1,0}, which represents the connections betweenthe subsequently generated node #3 and the previously generated nodes ina sequential manner, and {1,0} means that the subsequently generatednode #3 is connected with node #1 but not connected with node #2. Here,θ₃ is set as {0.8, 0.1}, which means that the probability of node #1 andnode #3 being connected is 0.8 and the probability of node #2 and node#3 being connected is 0.1.

At h3, node #3 is illustrated which, based on S₃ ^(π), is connected withnode #1 and not connected with node #2.

S₄ ^(π) is set as {0, 1, 1}, which represents the connections betweenthe subsequently generated node #4 and the previously generated nodesand means that node #4 is not connected with node #1 but is connectedwith node #2 and node #3. θ₄ is set as {0.2, 0.7, 0.8}, which representsthe probability information for the connections of S₄ ^(π).

At h4, node #4 is illustrated which, based on S₄ ^(π), is connected withnodes #2 and #3 but not connected with node #1.

S_(i) ^(π) forming the graph topology vector can be expressed asEquation 2 shown below.S ₁ ^(π)=(a _(1,i) ^(π) , . . . ,a _(i−1,i) ^(π)),∀iϵ{2, . . . ,|V _(O)|+|V _(M)|}  [Equation 2]

In Equation 2 above, a_(u,v) ^(π) represents the connection with the(u,v)-th node.

Also, the probability distribution for the graph topology vectors can beexpressed as Equation 3 shown below.

$\begin{matrix}{{p\left( S^{\pi} \right)} = {\prod\limits_{i = 2}^{{V_{O}} + {V_{M}}}\;{p\left( {{S_{i}^{\pi}❘S_{1}^{\pi}},\cdots\;,S_{i - 1}^{\pi}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

The probability distribution of Equation 3 above, which may be aprobability distribution for graph topolgies, can be defined as theprobability of the graph of a particular topology following the learnedgraph structure and can be obtained in the form of a conditionalprobability as in Equation 3 above.

According to an embodiment of the disclosure, the graph-generatingneural network 500 can include a network of an RNN structure.

A graph-generating neural network 500 of an RNN structure may learnprobability information for graph topologies and connections of thegraph topologies. More specifically, the graph-generating neural networkcan be defined as learning two functions, f_(trans) related to topologyand Gut related to connection probability, where f_(trans) and Gut canbe defined by Equation 4 and Equation 5 shown below.h _(i) =f _(trans)(h _(i−1) ,S _(i) ^(π))  [Equation 4]θ_(i+1) =f _(out)(h _(i))  [Equation 5]

f_(trans) and f_(out) of the graph-generating neural network may beformed by learning, and the weights of these functions may be determinedby learning.

From the graph-generating neural network learned using a referencenetwork, the connection probability vectors, θ, may be obtained, and anembodiment of the disclosure may complete the target network using theobtained θ.

As described above, an embodiment of the disclosure may use the networkcompletion neural network module 510 to perform network completion, andthe connection probability vectors θ may be inputted to the networkcompletion neural network module 510.

The target network G_(O) including missing nodes may be formed by usingthe neural network of the network completion neural network module 510and the connection probability vectors θ.

FIG. 7 is a diagram conceptually illustrating structure of a networkcompletion neural network module 510 according to an embodiment of thedisclosure.

Referring to FIG. 7 , a network completion neural network moduleaccording to an embodiment of the disclosure may include a neuralnetwork unit 700 and a selection unit 710.

The neural network unit 700 may be a neural network that follows theweights of the already learned graph-generating neural network 500. Anode sequence including missing nodes may be inputted to the neuralnetwork unit 700, and the neural network unit 700 may complete the graphstructure based on the learned weights.

FIG. 8 shows an example of a graph completion process at a neuralnetwork unit 700 according to an embodiment of the disclosure.

FIG. 8 illustrates an example in which three nodes A, B, and C arevisible nodes and D and E are missing nodes. The number of missing nodesmay be configured beforehand and a particular sequence of nodes,including missing nodes, may be inputted to the neural network unit 700according to an embodiment of the disclosure.

FIG. 8 illustrates an example in which the sequence for painting(generating) nodes is {E, D, A, C, B}. Here, E and D are missing nodesof which the connections are unknown.

As illustrated in FIG. 8 , the neural network unit 700 may complete thenetwork in a particular sequence by using f_(trans) and f_(out), whichfollow the already learned weights, to infer S_(i) ^(π). In FIG. 8 , theconnections of D and E, which are missing nodes, may initially be markedas ?, because these are unknown, but S_(i) ^(π) may be inferred by usingthe learned f_(trans) and f_(out).

The neural network unit 700 may perform network completion for allpossible sequences including the missing nodes to output candidatecomplete networks. If there are three visible nodes and two missingnodes as in FIG. 8 , the total number of permutations would be 5!, andthere would be a total of 120 cases.

The selection unit 710 may perform the final network completion byselecting one candidate complete network from among the multiple numberof candidate complete networks. The selection unit 710 may select thefinal complete network by using the connection probability vectors θobtained from the learned graph-generating neural network 500.

From among each of the candidate complete networks, the selection unit710 may select the candidate complete network which, based on theconnection probability vectors, has the highest similarity probabilitywith the inputted target network G_(O). Such selection of the completenetwork can be expressed as Equation 6 shown below.

$\begin{matrix}{\hat{G} = {\underset{G}{argmax}\mspace{14mu}{P\left( {{G❘G_{O}},\theta} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

As Equation 6 above, the selection unit 710 may select the completenetwork G of a particular sequence having a structure probabilisticallythe most similar to the target network from among the candidate completenetworks G, based on the connection probability vectors θ.

The network completion based on the present disclosure described withreference to FIG. 7 and FIG. 8 is for illustration only and can bemodified in various ways. For example, the candidate complete networksmay not necessarily be outputted for all possible permutations. Theselection process can be performed after outputting the candidatecomplete networks only for certain potentially feasible permutations.

The description of the disclosure provided above is for illustrativepurposes only, and a person having ordinary skill in the field of art towhich the present disclosure pertains would understand that variationsinto different specific forms can be easily implemented withoutdeparting from the technical spirit or changing the essential featuresof the disclosure.

Therefore, it should be understood that, in all aspects, the embodimentspresented above all illustrative only and are not limiting.

For example, an element described as having an integrated form can bepracticed in a distributed form, and likewise, elements described ashaving a distributed form can be practiced in a combined form.

The scope of the disclosure is defined by the scope of claims below, andit is to be understood that the meaning and scope of the claims as wellas all modifications and variations derived from their equivalentconcepts are encompassed within the scope of the present disclosure.

What is claimed is:
 1. A network completion device comprising: a neuralnetwork unit configured to receive input of a target network havingunrevealed missing nodes, infer connections of the missing nodes by wayof a neural network, and output a plurality of candidate completenetworks according to various node sequences; and a selection unitconfigured to select one of the plurality of candidate complete networksoutputted by the neural network unit, wherein the neural network unitoutputs the plurality of candidate complete networks by using weights ofa graph-generating neural network, wherein the graph-generating neuralnetwork has a learned graph structure of reference networks having thesame attributes as attributes of the target network, the selection unituses a connection probability vector obtained from the graph-generatingneural network to select a candidate complete network probabilisticallyhaving a structure closest to a structure of the target network based onthe connection probability vector, and the selection unit selects one ofthe candidate complete networks based on an equation shown below:${\hat{G} = {\underset{G}{argmax}\mspace{14mu}{P\left( {{G❘G_{O}},\theta} \right)}}},$where G represents the candidate complete networks, G₀ represents thetarget network, θ represents the connection probability vector, and Ĝrepresents the selected candidate complete network.
 2. The networkcompletion device of claim 1, wherein sequence information is inputtedto the neural network unit, the sequence information configuring anarbitrary sequence for observable nodes and missing nodes requiringinferring in the target network, and the neural network unit outputs thecandidate complete networks according to the sequence information. 3.The network completion device of claim 1, wherein the graph-generatingneural network configures the weights by learning a function (ftrans)related to a topology of the reference networks and a function (fout)related to a connection probability.
 4. The network completion device ofclaim 3, wherein the graph-generating neural network generates a graphby using the function related to the topology of the reference networksand the function related to the connection probability to sequentiallypaint nodes.
 5. The network completion device of claim 1, wherein theconnection probability vector includes probability information relatedto connections of a graph topology generated by way of thegraph-generating neural network.
 6. A network completion methodcomprising: (a) receiving input of a target network having unrevealedmissing nodes, inferring connections of the missing nodes by way of aneural network, and outputting a plurality of candidate completenetworks according to various node sequences; and (b) selecting one ofthe plurality of candidate complete networks outputted in said step (a),wherein said step (a) outputs the plurality of candidate completenetworks by using weights of a graph-generating neural network, whereinthe graph-generating neural network has a graph structure of referencenetworks having the same attributes as attributes of the target network,said step (b) uses a connection probability vector obtained from thegraph-generating neural network to select a candidate complete networkprobabilistically having a structure closest to a structure of thetarget network based on the connection probability vector, and said step(b) selects one of the candidate complete networks based on an equationshown below:${\hat{G} = {\underset{G}{argmax}\mspace{14mu}{P\left( {{G❘G_{O}},\theta} \right)}}},$where G represents the candidate complete networks, G₀ represents targetnetwork, θ represents the connection probability vector, and Ĝrepresents the selected candidate complete network.
 7. The networkcompletion method of claim 6, wherein sequence information is inputtedin said step (a), the sequence information configuring an arbitrarysequence for observable nodes and missing nodes requiring inferring inthe target network, and the candidate complete networks are outputtedaccording to the sequence information.
 8. The network completion methodof claim 6, wherein the graph-generating neural network configures theweights by learning a function (ftrans) related to a topology of thereference networks and a function (fout) related to a connectionprobability.
 9. The network completion method of claim 8, wherein thegraph-generating neural network generates a graph by using the functionrelated to the topology of the reference networks and the functionrelated to the connection probability to sequentially paint nodes. 10.The network completion method of claim 6, wherein the connectionprobability vector includes probability information related toconnections of a graph topology generated by way of the graph-generatingneural network.